Match the equation of a parabola to its focus and directrix.

Rewrite as perfect squares

20y-120=-(x+7)²

20*(y-6)=-(x+7)²

-20*(y-6)=(x+7)²> (x-h)²=4p*(y-k)

vertex (h,k)> (-7,6)

4p=-20> p=-5

focus (h, k+p)> (-7,6-5)> (-7,1)

directrix y=k-p> 6+5> 11

the answer Part 1) is

focus (-7,1)

directrix y=11

Part 2) 

x=(-y²/12)-(y/3)+14/3> multiply by 12> 12x=-y²-4y+56

12x-56=-(y²+4y)

Complete the square. Remember to balance the equation by adding the same constants to each side

12x-56-4=-(y²+4y+4)

12x-60=-(y+2)²

12*(x-5)=-(y+2)²

-12*(x-5)=(y+2)²

the vertex is (5, -2)

4p=-12> p=-3

focus (h+p, k)> (5-3,-2)> (2,-2)

directrix x=h-p> x=5+3> x=8

the answer Part 2) is

focus (2,-2)

directrix x=8

Part 3)

y=(-x²/20)-(7x/10)+11/20> multiply by 20> 20y=-x²-14x+11

20y-11=-(x²+14x)

Complete the square. Remember to balance the equation by adding the same constants to each side

20y-11-49=-(x²+14x+49)

20y-60=-(x+7)²

20*(y-3)=-(x+7)²

-20*(y-3)=(x+7)²

the vertex is (-7,3)

4p=-20> p=-5

focus (h, k+p)> (-7, 3-5)> (-7, -2)

directrix y=k-p> y=3+5> y=8

the answer part 3) is

focus (-7, -2)

directrix y=8

Part 4) 

cosine

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)